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Moment about the origin

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Given that f(x)=x/2, where 0 < x < 2, please prove that the moment generating function is
M(z)=[(2z-1)exp(2z)+1]/2z^2, and please use it to prove that the kth moment about the origin is 2^(k+1)/(k+2) by expanding exponentials.

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Solution Summary

This solution proves that a moment generating function is M(z)=[(2z-1)exp(2z)+1]/2z^2.

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